# Rotational Motion of a shaft

## Homework Statement

A shaft is turning at 73.8 rad/s at time zero. Thereafter, its angular acceleration is given by
where t is the elapsed time. Calculate its angular speed at t = 2.58 s

## Homework Equations

1/2(Angular accel formula)+ 73.8t+0= theta final

## The Attempt at a Solution

do i take the integral of the accel formula then the velocity the plug in 2.58?

kuruman
Homework Helper
Gold Member
You need to integrate both sides of

dω = αdt

The limits of integration should be

73.8 to ω (left side) and 0 to 2.58 (right side)

After you integrate, solve for ω.

so i set 1/2(angular accel)= 73.8+ theta final? then take the integral?

kuruman
Homework Helper
Gold Member
so i set 1/2(angular accel)= 73.8+ theta final? then take the integral?
I never said that. I have no idea where you get that 1/2(angular accel) = 73.8 + theta final means something when it is not even dimensionally correct. Do the following integral and solve for ω. That's what I suggested in the first place.

$$\int_{73.8}^{\omega}d \omega=\int_{0}^{2.58}(-10.1-4.44 t) dt$$

whoa dude calm down. i appericiate the help but remember i was just asking a question, i already feel stupid enough as it is